Anniversaty Address of the President, 1840. 151 



Professor Hansen's general researches in physical astronomy, the 

 other on Professor Bessel's and Mr. Henderson's observations on the 

 parallax of those remarkable double stars, 61 Cygni and a Centaur i 

 — observations which it would appear, beyond question, have 

 brought us to the very threshold of that long-sought portal which is 

 to open to us a measurable pathway into regions where the wings 

 of fancy have hitherto been overborne by the weight or baffled by the 

 vagueness of the illimitable and the infinite. 



M. Hansen's researches on the lunar and planetary theories are 

 every way most remarkable, and seem likely to lead to results of the 

 utmost generality and importance. He has attacked the great 

 problem of three bodies (extended, in the conception and application 

 of his methods, to the mutual perturbations of four) by a method 

 entirely novel in its idea, although based on and starting from La- 

 grange's idea of the variation of the elements. Of this method, it 

 would not be easy, in words unaided by symbolic expression, to give 

 any distinct account ; but its principle may be stated in general 

 terms, as assuming not the elliptic elements, but the elliptic time, to 

 be subject to perturbation ; or, in other words, as considering the 

 perturbed co-ordinates, each to arise from the combination of inva- 

 riable elements with a varied or perturbed time, the amount of whose 

 variation shall exactly account for all that the variation of the ele- 

 ments accounts for in Lagrange's method. The mere mention of 

 this refined and abstruse mode of conceiving the problem must suf- 

 fice to show, that, to carry it into eflFect, must require at every step 

 a contention of mind, a degree of intellectual effort, far surpassing 

 what is required for the mere management of algebraic symbols and 

 developments, however intricate. 



Whatever be the skill and dexterity, however, exhibited by the 

 author of this truly original conception, and whatever promise it 

 must be considered as holding out for the future advancement of our 

 knowledge in this intricate research, it can hardly yet be regarded 

 as having attained that extent of development which it will require 

 to supersede in the construction of tables, and the actual calculation 

 of the lunar and planetary perturbations, the methods already in use, 

 which the researches of Clairaut, Laplace, Lagrange, Poisson, Damoi- 

 seau, and Plana, have wrought up to such a pitch of practical per- 

 fection. Hansen's theory appears to afford what, in the actual state 

 of our knowledge, must be regarded as most precious — a new handle 

 by which to seize this refractory problem — one of universal applica- 

 bility and gigantic power and purchase, but of which the manage- 

 ment is not yet fully reduced to practice, and of which even the au- 

 thor himself can scarcely yet be said to have acquired the entire 

 mastery. In the theory of Jupiter and Saturn, indeed, the final 

 numerical results are obtained, and tables calculated ; but in the 

 lunar theory, which (in the words of Mr. Airy) " must be considered 

 as the ground of his chief analytical triumph, there exist at present 

 only what may be termed the foundations for such a theory." " No 

 man living" (I continue to use the words of the eminent geometer 

 last-mentioned), " No man living, probably, except M. Hansen him- 

 self, could work it into a complete lunar theory ; and the exhibition of 



